In a triangle ABc C = 90 degrees A = 45 degrees AB = 8cm Find the length of the median BM.
| September 27, 2021 | education
Since in a right-angled triangle ABC the angle BAC = 450, then the angle ABC = 45, then the triangle ABC is isosceles.
Determine the length of the legs AC and BC.
SinВАС = ВС / АВ.
BC = AB * Sin45 = 8 * √2 / 2 = 4 * √2 cm.
BC = AC = 4 * √2 cm.
Since BM is the median, then AM = CM = AC / 2 = 4 * √2 / 2 = 2 * √2 cm.
From the right-angled triangle of the BCM, by the Pythagorean theorem, we determine the length of the hypotenuse of the BM.
BM ^ 2 = BC ^ 2 + CM ^ 2 = (4 * √2) ^ 2 + (2 * √2) ^ 2 = 32 + 8 = 40.
BM = 2 * √10 cm.
Answer: The length of the median BM is 2 * √10 cm.
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